Improper affine spheres and δ-invariants
We introduce an inequality for graph hypersurfaces and prove a decomposition theorem in case equality holds.
Indefinite affine hyperspheres admitting a pointwise symmetry. I.
Indefinite affine hyperspheres admitting a pointwise symmetry. II.
Inequalities for radial Blaschke-Minkowski homomorphisms
We establish Brunn-Minkowski type inequalities for radial Blaschke-Minkowski homomorphisms, which in special cases yield some new results for intersection bodies. Moreover, we obtain two monotonicity inequalities for radial Blaschke-Minkowski homomorphisms.
Infinitesimal rigidity of surfaces in
Inner parallel curves and domains in the equiaffine geometry.
Invariance groups of relative normals
We investigate a two-parameter family of relative normals that contains Manhart's one-parameter family and the centroaffine normal. The invariance group of each of these normals is classified, and variational problems are studied. The results are Euler-Lagrange equations for the hypersurfaces that are critical with respect to the area functionals of the induced and semi-Riemannian volume forms and a classification of the critical hyperovaloids in the two-parameter family.